Model-free trackers can track arbitrary objects based on a single (bounding-box) annotation of the object. Whilst the performance of model-free trackers has recently improved significantly, simultaneously tracking multiple objects with similar appearance remains very hard. In this paper, we propose a new multi-object model-free tracker (using a tracking-by-detection framework) that resolves this problem by incorporating spatial constraints between the objects. The spatial constraints are learned along with the object detectors using an online structured SVM algorithm. The experimental evaluation of our structure-preserving object tracker (SPOT) reveals significant performance improvements in multi-object tracking. We also show that SPOT can improve the performance of single-object trackers by simultaneously tracking different parts of the object. Moreover, we show that SPOT can be used to adapt generic, model-based object detectors during tracking to tailor them towards a specific instance of that object.